Density-functional theory for internal magnetic fields

  title={Density-functional theory for internal magnetic fields},
  author={Erik I Tellgren},
  journal={Physical Review A},
  • E. Tellgren
  • Published 3 November 2017
  • Physics
  • Physical Review A
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current-density functional theory and an alternative to the paramagnetic current density-functional theory due to… 

Figures from this paper

Revisiting density-functional theory of the total current density

It is proved that Diener’s formulation is unfortunately not capable of reproducing the correct ground-state energy and, furthermore, that the suggested construction of a Hohenberg–Kohn map contains an irreparable mistake.

Kohn-Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability.

This article extends Moreau-Yosida regularization to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects, including a well-defined Kohn-Sham iteration scheme with a partial convergence result.

Kohn–Sham energy decomposition for molecules in a magnetic field

ABSTRACT We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent

Density–wave-function mapping in degenerate current-density-functional theory

We show that the particle density, $\rho(\mathbf{r})$, and the paramagnetic current density, $\mathbf{j}^{p}(\mathbf{r})$, are not sufficient to determine the set of degenerate ground-state wave

Force balance approach for advanced approximations in density functional theories.

This work proposes a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials based on equations of motion of current quantities and is feasible both in the ground-state and the time-dependent settings.

Benchmarking Density Functional Approximations for Diamagnetic and Paramagnetic Molecules in Nonuniform Magnetic Fields

A more fine-grained classification of molecular systems on the basis of their response to generally nonuniform magnetic fields is proposed and the relation of orientation to different qualitative responses is considered.

Benchmarking the Accuracy of the Direct Random Phase Approximation and σ-Functionals for NMR Shieldings.

The results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree-Fock exchange in the functional.

Unique continuation for many-body Schr\"odinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian

We prove the strong unique continuation property for many-body Pauli operators with external potentials, interaction potentials and magnetic fields in $L^p_{\rm loc}(\mathbb{R}^d)$, and with magnetic

Unique continuation for the magnetic Schrödinger equation

Abstract The unique‐continuation property from sets of positive measure is here proven for the many‐body magnetic Schrödinger equation. This property guarantees that if a solution of the Schrödinger

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any



Uniform magnetic fields in density-functional theory.

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory

Nonexistence of a Hohenberg-Kohn variational principle in total current-density-functional theory

This thesis contains four articles related to mathematical aspects of Density Functional Theory.In Paper A, the theoretical justification of density methods formulated with current densities is

Magnetic-Field Density-Functional Theory (BDFT): Lessons from the Adiabatic Connection.

It is demonstrated that adiabatic-connection curves at different field strengths resemble one another closely provided each curve is calculated at the equilibrium geometry of that field strength, which implies that density-functional approximations may be applied to systems in strong fields, without the need to treat additional static correlation.

Non-perturbative calculation of molecular magnetic properties within current-density functional theory.

A novel implementation of Kohn-Sham density-functional theory utilizing London atomic orbitals as basis functions is presented, which is the first fully self-consistent implementation of the latter for molecules in very strong magnetic fields.

Choice of basic variables in current-density-functional theory

The selection of basic variables in current-density-functional theory and formal properties of the resulting formulations are critically examined. Focus is placed on the extent to which the

Current-density-functional theory for a nonrelativistic electron gas in a strong magnetic field

A current-density-functional theory is formulated in terms of the physical gauge-invariant current density instead of the 'paramagnetic' or canonical current density used previously by Vignale and

Density Functionals in the Presence of Magnetic Field

In this paper density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density, $\rho$, and paramagnetic current

Quantum electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field.

Exact density functionals for two-electron systems in an external magnetic field.

This work constructs the correlated electron density and paramagnetic current density, the exact Kohn-Sham orbitals, and the exact DFT and CDFT exchange-correlation energies and potentials, and illustrates how the CDFT vorticity variable nu is a computationally difficult quantity which may not be appropriate in practice to describe the external B field effects on E(XC) and A( XC).

Density-functional theory of many-electron systems subjected to time-dependent electric and magnetic fields.

  • GhoshDhara
  • Physics
    Physical review. A, General physics
  • 1988
A time-dependent density-functional formalism is developed for many-electron systems subjected to external electric and magnetic fields with arbitrary time dependence. The single-particle current